Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-28T13:35:19.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Eigenvalue bounds for the Orr-Sommerfeld equation

Published online by Cambridge University Press:  28 March 2006

Daniel D. Joseph
Daniel D. Joseph
Affiliation:
Department of Aeronautics and Engineering Mechanics, University of Minnesota
Get access Rights & Permissions [Opens in a new window]

Abstract

Estimates of the eigenvalues C belonging to the manifold of solutions of the Orr-Sommerfeld equation are constructed by application of elementary isoperimetric inequalities. The inequalities also lead to a considerable improvement on the estimate of (αR) regions of linear stability given by Synge.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 3 , 2 September 1968 , pp. 617 - 621
Copyright
© 1968 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic stability of parallel flow of an inviscid fluid Adv. Appl. Mech. 9, 1–85.Google Scholar
Eagles, P. M. 1966 The stability of a family of Jeffery-Hamel solutions for divergent channel flow J. Fluid Mech. 24, 191–207.Google Scholar
HØILAND, E. 1953 On two-dimensional perturbation of linear flow. Geofys. Publ. 18, J. Fluid Mech. 16, 333–42. See also Drazin & Howard (1966).Google Scholar
Joseph, D. D. 1966 Nonlinear stability of the Boussinesq equations by the method of energy Arch. Rat. Mech. Anal. 22, 163–84.Google Scholar
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Pai, S. I. 1954 On a generalization of Synge's criterion for sufficient stability of plane parallel flows Quart. Appl. Math. 12, 203–6.Google Scholar
Rayleigh, LORD 1878 Theory of Sound. 2nd ed., vol. 1, paragraph 174. New York: Dover 1945.
Synge, J. L. 1938 Hydrodynamical stability Semicentenn. Publ. Amer. Math. Soc. 2, 227–69.Google Scholar